Here\'s what I\'d like:
REPO-A
/.git
/otherFiles
/REPO-B
/.git
/moreFiles
I want to be able to push all of REPO-A\'s
Yes, you can do exactly what you're asking with the file hierarchy you drew. Repo-B will be independant and have no knowledge of Repo-A. Repo-A will track all changes in it's own files and Repo-B's files.
However, I would not recommend doing this. Every time you change files and commit in Repo-B you'll have to commit in Repo-A. Branching in Repo-B will mess with Repo-A and branching in Repo-A will be wonky (trouble removing folders, etc.). Submodules are definitely the way to go.